Project Network-based Data Analysis
Annalisa Xamin
Install and load R packages
if (!require("BiocManager", quietly = TRUE))
install.packages("BiocManager")
if (!require("GEOquery", quietly = TRUE))
BiocManager::install("GEOquery")
if (!require("rScudo", quietly = TRUE))
BiocManager::install("rScudo")
library(tidyverse)
library(dplyr)
library(GEOquery)
library(rScudo)
library(plotly)
library(sessioninfo)
library(ggplot2)
library(factoextra)
library(useful)
library(umap)
my_colors <- c("#2e005d", "#5c008b", "#8e008b", "#ff8300", "#ff6200", "#d1105a", "#05a8aa")R session information
Print the R session information for reproducibility.
print('Reproducibility information:') ## [1] "Reproducibility information:"Sys.time()## [1] "2024-10-16 10:37:45 CEST"proc.time()## user system elapsed
## 1.679 0.152 2.297options(width = 120)
session_info()## ─ Session info ───────────────────────────────────────────────────────────────────────────────────────────────────────
## setting value
## version R version 4.4.0 (2024-04-24)
## os macOS 15.0.1
## system aarch64, darwin23.4.0
## ui unknown
## language (EN)
## collate en_US.UTF-8
## ctype en_US.UTF-8
## tz Europe/Rome
## date 2024-10-16
## pandoc 3.1.11 @ /Applications/RStudio.app/Contents/Resources/app/quarto/bin/tools/aarch64/ (via rmarkdown)
##
## ─ Packages ───────────────────────────────────────────────────────────────────────────────────────────────────────────
## package * version date (UTC) lib source
## askpass 1.2.0 2023-09-03 [1] CRAN (R 4.4.0)
## Biobase * 2.64.0 2024-04-30 [1] Bioconductor 3.19 (R 4.4.0)
## BiocGenerics * 0.50.0 2024-04-30 [1] Bioconductor 3.19 (R 4.4.0)
## BiocManager * 1.30.25 2024-08-28 [1] CRAN (R 4.4.0)
## bslib 0.8.0 2024-07-29 [1] CRAN (R 4.4.0)
## cachem 1.1.0 2024-05-16 [1] CRAN (R 4.4.0)
## cli 3.6.3 2024-06-21 [1] CRAN (R 4.4.0)
## colorspace 2.1-1 2024-07-26 [1] CRAN (R 4.4.0)
## data.table 1.16.0 2024-08-27 [1] CRAN (R 4.4.0)
## digest 0.6.37 2024-08-19 [1] CRAN (R 4.4.0)
## dplyr * 1.1.4 2023-11-17 [1] CRAN (R 4.4.0)
## evaluate 0.24.0 2024-06-10 [1] CRAN (R 4.4.0)
## factoextra * 1.0.7 2020-04-01 [1] CRAN (R 4.4.0)
## fansi 1.0.6 2023-12-08 [1] CRAN (R 4.4.0)
## fastmap 1.2.0 2024-05-15 [1] CRAN (R 4.4.0)
## forcats * 1.0.0 2023-01-29 [1] CRAN (R 4.4.0)
## generics 0.1.3 2022-07-05 [1] CRAN (R 4.4.0)
## GEOquery * 2.72.0 2024-04-30 [1] Bioconductor 3.19 (R 4.4.0)
## ggplot2 * 3.5.1 2024-04-23 [1] CRAN (R 4.4.0)
## ggrepel 0.9.6 2024-09-07 [1] CRAN (R 4.4.0)
## glue 1.7.0 2024-01-09 [1] CRAN (R 4.4.0)
## gtable 0.3.5 2024-04-22 [1] CRAN (R 4.4.0)
## hms 1.1.3 2023-03-21 [1] CRAN (R 4.4.0)
## htmltools 0.5.8.1 2024-04-04 [1] CRAN (R 4.4.0)
## htmlwidgets 1.6.4 2023-12-06 [1] CRAN (R 4.4.0)
## httr 1.4.7 2023-08-15 [1] CRAN (R 4.4.0)
## jquerylib 0.1.4 2021-04-26 [1] CRAN (R 4.4.0)
## jsonlite 1.8.8 2023-12-04 [1] CRAN (R 4.4.0)
## knitr 1.48 2024-07-07 [1] CRAN (R 4.4.0)
## lattice 0.22-6 2024-03-20 [2] CRAN (R 4.4.0)
## lazyeval 0.2.2 2019-03-15 [1] CRAN (R 4.4.0)
## lifecycle 1.0.4 2023-11-07 [1] CRAN (R 4.4.0)
## limma 3.60.4 2024-07-17 [1] Bioconductor 3.19 (R 4.4.0)
## lubridate * 1.9.3 2023-09-27 [1] CRAN (R 4.4.0)
## magrittr 2.0.3 2022-03-30 [1] CRAN (R 4.4.0)
## Matrix 1.7-0 2024-03-22 [2] CRAN (R 4.4.0)
## munsell 0.5.1 2024-04-01 [1] CRAN (R 4.4.0)
## openssl 2.2.1 2024-08-16 [1] CRAN (R 4.4.0)
## pillar 1.9.0 2023-03-22 [1] CRAN (R 4.4.0)
## pkgconfig 2.0.3 2019-09-22 [1] CRAN (R 4.4.0)
## plotly * 4.10.4 2024-01-13 [1] CRAN (R 4.4.0)
## plyr 1.8.9 2023-10-02 [1] CRAN (R 4.4.0)
## png 0.1-8 2022-11-29 [1] CRAN (R 4.4.0)
## purrr * 1.0.2 2023-08-10 [1] CRAN (R 4.4.0)
## R6 2.5.1 2021-08-19 [1] CRAN (R 4.4.0)
## Rcpp 1.0.13 2024-07-17 [1] CRAN (R 4.4.0)
## readr * 2.1.5 2024-01-10 [1] CRAN (R 4.4.0)
## reticulate 1.39.0 2024-09-05 [1] CRAN (R 4.4.0)
## rlang 1.1.4 2024-06-04 [1] CRAN (R 4.4.0)
## rmarkdown 2.28 2024-08-17 [1] CRAN (R 4.4.0)
## rScudo * 1.20.0 2024-04-30 [1] Bioconductor 3.19 (R 4.4.0)
## RSpectra 0.16-2 2024-07-18 [1] CRAN (R 4.4.0)
## rstudioapi 0.16.0 2024-03-24 [1] CRAN (R 4.4.0)
## sass 0.4.9 2024-03-15 [1] CRAN (R 4.4.0)
## scales 1.3.0 2023-11-28 [1] CRAN (R 4.4.0)
## sessioninfo * 1.2.2 2021-12-06 [1] CRAN (R 4.4.0)
## statmod 1.5.0 2023-01-06 [1] CRAN (R 4.4.0)
## stringi 1.8.4 2024-05-06 [1] CRAN (R 4.4.0)
## stringr * 1.5.1 2023-11-14 [1] CRAN (R 4.4.0)
## tibble * 3.2.1 2023-03-20 [1] CRAN (R 4.4.0)
## tidyr * 1.3.1 2024-01-24 [1] CRAN (R 4.4.0)
## tidyselect 1.2.1 2024-03-11 [1] CRAN (R 4.4.0)
## tidyverse * 2.0.0 2023-02-22 [1] CRAN (R 4.4.0)
## timechange 0.3.0 2024-01-18 [1] CRAN (R 4.4.0)
## tzdb 0.4.0 2023-05-12 [1] CRAN (R 4.4.0)
## umap * 0.2.10.0 2023-02-01 [1] CRAN (R 4.4.0)
## useful * 1.2.6.1 2023-10-24 [1] CRAN (R 4.4.0)
## utf8 1.2.4 2023-10-22 [1] CRAN (R 4.4.0)
## vctrs 0.6.5 2023-12-01 [1] CRAN (R 4.4.0)
## viridisLite 0.4.2 2023-05-02 [1] CRAN (R 4.4.0)
## withr 3.0.1 2024-07-31 [1] CRAN (R 4.4.0)
## xfun 0.47 2024-08-17 [1] CRAN (R 4.4.0)
## xml2 1.3.6 2023-12-04 [1] CRAN (R 4.4.0)
## yaml 2.3.10 2024-07-26 [1] CRAN (R 4.4.0)
##
## [1] /opt/homebrew/lib/R/4.4/site-library
## [2] /opt/homebrew/Cellar/r/4.4.0/lib/R/library
##
## ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────Data selection
The analysis will use the dataset GSE20437 obtained from GEO.The dataset is generated from Affymetrix HU133A microarrays and contains 42 tissue samples.
In detail, the data includes:
18 reduction mammoplasty (RM) breast epithelium samples,
18 histologically normal (HN) epithelial samples from breast cancer patients (9 ER+ and 9 ER-), and
6 histologically normal epithelial samples from prophylactic mastectomy patients.
Note that sample numbers correspond to individual patient samples.
# download the GSE20437 expression data series
gse <- getGEO("GSE20437", destdir= './data/', getGPL = F)# getGEO returns a list of expression objects, but...
length(gse) ## [1] 1# shows us there is only one object in it.
# We assign it to the same variable.
gse <- gse[[1]]# extract metadata
metadata <- data.frame(gse@phenoData@data)
# save metadata to csv file
#write.csv(metadata, file = 'metadata.csv', row.names = TRUE)p <- ggplot(metadata, aes(x=disease.state.ch1, fill=specimen.ch1))+
geom_bar()+
scale_fill_manual(values = my_colors[c(1,4,6,7)])
p + labs(x = "Group") 
Exploratory analysis
# show what we have:
show(gse)## ExpressionSet (storageMode: lockedEnvironment)
## assayData: 22283 features, 42 samples
## element names: exprs
## protocolData: none
## phenoData
## sampleNames: GSM512539 GSM512540 ... GSM512580 (42 total)
## varLabels: title geo_accession ... tissue:ch1 (38 total)
## varMetadata: labelDescription
## featureData: none
## experimentData: use 'experimentData(object)'
## pubMedIds: 20197764
## Annotation: GPL96The actual expression data are accessible in the exprs
section of gse, an Expression Set and the generic data
class that BioConductor uses for expression data.
head(exprs(gse)) ## GSM512539 GSM512540 GSM512541 GSM512542 GSM512543 GSM512544 GSM512545 GSM512546 GSM512547 GSM512548 GSM512549
## 1007_s_at 2461.4 3435.7 1932.5 2377.7 3055.3 2978.1 2348.5 2963.9 2776.9 3088.9 3033.3
## 1053_at 26.7 159.0 31.2 140.7 69.9 98.5 37.0 59.9 86.7 107.2 64.0
## 117_at 82.6 243.4 150.2 95.1 209.3 103.4 91.2 168.4 162.7 203.2 143.7
## 121_at 942.3 897.5 840.8 870.9 685.4 791.8 886.5 954.2 843.1 775.3 847.6
## 1255_g_at 71.8 87.9 75.4 58.1 31.8 40.3 70.5 43.3 51.6 42.6 74.9
## 1294_at 630.2 571.4 346.3 679.9 1289.3 421.1 417.6 811.6 778.1 393.2 995.4
## GSM512550 GSM512551 GSM512552 GSM512553 GSM512554 GSM512555 GSM512556 GSM512557 GSM512558 GSM512559 GSM512560
## 1007_s_at 3037.1 3545.8 3322.6 1963.7 3609.6 2078.9 4138.6 4260.7 2453.6 2709.0 2612.5
## 1053_at 82.9 97.7 69.7 82.0 45.6 84.5 31.7 37.4 82.4 204.8 119.3
## 117_at 113.5 80.0 186.4 106.6 145.6 144.4 133.6 278.6 173.0 147.8 186.0
## 121_at 912.2 911.6 862.4 705.0 984.6 853.8 846.8 1273.0 833.6 908.1 806.2
## 1255_g_at 53.7 30.5 15.2 42.5 76.6 88.2 90.6 65.8 25.8 77.5 84.3
## 1294_at 987.7 938.5 924.6 480.8 1054.1 632.0 448.0 1345.2 1248.9 405.7 647.5
## GSM512561 GSM512562 GSM512563 GSM512564 GSM512565 GSM512566 GSM512567 GSM512568 GSM512569 GSM512570 GSM512571
## 1007_s_at 4340.1 3155.3 2390.3 2738.8 3233.1 2836.6 2915.4 3457.5 2798.7 4370.2 2467.3
## 1053_at 76.7 100.3 115.4 14.1 47.6 77.1 47.1 47.0 83.2 40.2 80.3
## 117_at 168.0 95.2 73.6 122.7 107.6 120.9 143.4 92.5 72.1 131.8 156.4
## 121_at 827.0 629.4 709.2 305.6 877.4 425.7 643.8 771.3 681.1 812.7 533.4
## 1255_g_at 87.9 44.6 59.3 12.0 82.1 59.2 62.2 28.3 97.6 8.1 17.9
## 1294_at 2218.1 1321.1 606.7 1709.9 980.8 1268.4 955.8 1157.5 888.6 1130.8 905.1
## GSM512572 GSM512573 GSM512574 GSM512575 GSM512576 GSM512577 GSM512578 GSM512579 GSM512580
## 1007_s_at 3669.5 3310.1 3942.2 4520.4 3596.1 2989.0 3164.5 2764.3 4258.5
## 1053_at 24.1 8.8 44.6 54.7 56.7 89.9 63.4 57.0 59.5
## 117_at 165.8 141.6 97.1 132.7 124.3 210.5 131.4 89.6 123.3
## 121_at 746.9 1090.3 1008.7 718.6 988.4 295.9 957.3 630.8 869.2
## 1255_g_at 53.0 39.9 11.0 50.2 60.0 34.3 33.5 61.7 50.4
## 1294_at 1138.5 483.0 1326.5 1179.4 668.3 863.2 1055.5 1287.6 1127.8To conveniently access the data rows and columns present in
exprs(gse), this matrix is assigned to its own variable
ex.
# exprs (gse) is a matrix that we can assign to its own variable, to
# conveniently access the data rows and columns
ex <- exprs(gse)
dim(ex) # 42 sample, 22283 genes## [1] 22283 42The dataset contains gene expression data of 22283 genes (rows) from 42 patients (columns).
Pre-processing
# Analyze value distributions
boxplot(ex, main = 'Boxplot of the data before normalization',
xlab = "Samples",
ylab = "Expression Value",
varwidth = TRUE
)
The boxplot shows that scaling is necessary. So, in this case, I try to apply a log transformation to the data.
ex2<-log(ex)
ex2 <- na.omit(as.matrix(ex2))
#dim(ex2) # 22283 42 same as before
boxplot(ex2, main = 'Boxplot of the data after applying a logarithmic transformation',
xlab = "Samples",
ylab = "Expression Value"
)
Boxplot of the data after applying a logarithmic transformation
From the boxplot after the log transformation, I can see that there is some variation in the median of the samples. So, I try to apply a median normalization to the data after the log transformation.
# MEDIAN NORMALIZATION
channel.medians=apply(log(ex),2,median)
normalized.log.ex=sweep(log(ex),2,channel.medians,"-")
# boxplot post median normalization on ex
boxplot(normalized.log.ex,
main = 'Boxplot of the data after median normalization',
xlab = "Samples",
ylab = "Expression Value")
Boxplot of the data after median normalization
PCA
PCA is a dimensionality reduction technique that allows to condense thousands of dimensions into just two or three. For the dataset’s samples, the PCA scores display the coordinates in relation to these additional dimensions.
pca <- prcomp(t(normalized.log.ex))
summary(pca)## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10
## Standard deviation 38.8020 23.47065 20.63892 19.54327 18.43330 15.97431 15.54787 15.25339 14.95988 13.82648
## Proportion of Variance 0.1791 0.06552 0.05067 0.04543 0.04042 0.03035 0.02875 0.02767 0.02662 0.02274
## Cumulative Proportion 0.1791 0.24461 0.29527 0.34070 0.38112 0.41147 0.44023 0.46790 0.49452 0.51726
## PC11 PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20
## Standard deviation 13.67761 13.63388 13.39954 13.05683 12.96288 12.78929 12.64910 12.48152 12.32645 12.13869
## Proportion of Variance 0.02225 0.02211 0.02136 0.02028 0.01999 0.01946 0.01903 0.01853 0.01807 0.01753
## Cumulative Proportion 0.53951 0.56162 0.58298 0.60326 0.62324 0.64270 0.66173 0.68026 0.69833 0.71586
## PC21 PC22 PC23 PC24 PC25 PC26 PC27 PC28 PC29 PC30
## Standard deviation 12.04722 11.97088 11.90374 11.69483 11.60734 11.57222 11.46507 11.15870 11.04915 10.99769
## Proportion of Variance 0.01726 0.01705 0.01685 0.01627 0.01603 0.01593 0.01564 0.01481 0.01452 0.01439
## Cumulative Proportion 0.73312 0.75017 0.76702 0.78329 0.79932 0.81525 0.83088 0.84569 0.86021 0.87460
## PC31 PC32 PC33 PC34 PC35 PC36 PC37 PC38 PC39 PC40 PC41
## Standard deviation 10.68517 10.45191 10.25430 10.13818 9.9583 9.68456 9.50070 9.42259 9.3053 9.17335 8.95347
## Proportion of Variance 0.01358 0.01299 0.01251 0.01223 0.0118 0.01116 0.01074 0.01056 0.0103 0.01001 0.00954
## Cumulative Proportion 0.88818 0.90117 0.91368 0.92591 0.9377 0.94886 0.95960 0.97016 0.9805 0.99046 1.00000
## PC42
## Standard deviation 6.784e-14
## Proportion of Variance 0.000e+00
## Cumulative Proportion 1.000e+00screeplot(pca)
To get the summary of the PCA and the plot showing the variance explained by the first 10 components, it is possible to use the functions commented in the chunks above.
However, using ggplot2 and factoextra
packages is possible to get a more concise and informative plot
reporting the same information.
pcaVar <- get_eig(pca)
pcaVar <- pcaVar$variance.percent[1:10]
screeDf <- data.frame("Dimensions" = as.factor(seq(1,10)),
"Percentages" = pcaVar,
"Labels" = paste(round(pcaVar, 2), "%"))
p <- ggplot(data = screeDf, aes(x=Dimensions, y=Percentages))+
geom_bar(stat = "identity", fill = "#d1105a")+
geom_text(aes(label=Labels), vjust=-0.5, color="black", size=3.6)+
ggtitle("Scree Plot")+
ylab("Percentage of variance explained")+
scale_x_discrete(labels = as.factor(seq(1,10)))
p
The scree plot shows that the first dimensions on the left are the more important because the percentage of variance explained by them is higher. The remaining principal components account for a very small proportion of the variability and are probably unimportant.
Let’s try to plot the PCA, looking if we can see a separation between Control and Breast Cancer groups.
# draw PCA plot control VS breast cancer
group <- c(rep("cadetblue1",18), rep("red",18), rep("cadetblue1",6) )
plot(pca$x[,1], pca$x[,2], xlab="PCA1", ylab="PCA2", main="PCA for components 1 and 2", type="p", pch=10, col=group)
text(pca$x[,1], pca$x[,2], rownames(pca$data), cex=0.75)
legend("topleft", col=c("cadetblue1","red"), legend = c("Control", "Breast Cancer"),
pch = 20, bty='n', cex=.55)
Let’s try to add the control subtypes. The vector group used in the PCA plot is based on the data. The samples corresponding to the colors are the following:
Light blue: reduction mammoplasty (RM) breast epithelium samples
Red: histologically normal (HN) epithelial samples from breast cancer patient
Purple: histologically normal breast epithelium (NlEpi) from prophylactic mastectomy patient samples
# draw PCA plot
group <- c(rep("cadetblue1",18), rep("red",18), rep("purple",6) ) # vector of colors based on the order of my data
plot(pca$x[,1], pca$x[,2], xlab="PCA1", ylab="PCA2", main="PCA for components 1 and 2", type="p", pch=10, col=group)
text(pca$x[,1], pca$x[,2], rownames(pca$data), cex=0.75)
legend("topleft", col=c("cadetblue1","red","purple"), legend = c("Reduction Mammoplasty", "Breast Cancer", "Prophylactic Mastectomy"),
pch = 20, bty='n', cex=.55)
Then, I try to see if there is a separation also inside different types of Breast Cancer.
# draw PCA plot with all subtypes
group <- c(rep(my_colors[7],18), rep(my_colors[4],9), rep(my_colors[1],9), rep(my_colors[6],6) ) # vector of colors based on the order of my data
plot(pca$x[,1], pca$x[,2], xlab="PCA1", ylab="PCA2", main="PCA for components 1 and 2", type="p", pch=10, col=group)
text(pca$x[,1], pca$x[,2], rownames(pca$data), cex=0.75)
legend("topleft", col=c(my_colors[7],my_colors[4],my_colors[1],my_colors[6]), legend = c("Reduction Mammoplasty", "ER+ Breast Cancer", "ER- Breast Cancer", "Prophylactic Mastectomy"),
pch = 20, bty='n', cex=.55)
Interactive PCA plot
Let’s try to explore an interactive PCA plot.
components<-pca[["x"]]
components<-data.frame(components)
type<-c(rep("RM", 18), rep("HN",18), rep("NlEpi",6))
components<-cbind(components, type )
fig <- plot_ly(components, x=~PC1, y=~PC2,
color=type,colors=c('cadetblue1', 'red','purple'),
type='scatter',mode='markers')
figfig2 <- plot_ly(components, x=~PC1, y=~PC2, z=~PC3,
color=type, colors=c('cadetblue1', 'red','purple'),
mode='markers', marker = list(size = 4))
fig2fig3 <- plot_ly(components, x=~PC1, y=~PC3,
color=type, colors=c('cadetblue1', 'red','purple'),
type='scatter',mode='markers')
fig3UMAP
umap_data <- umap::umap(t(normalized.log.ex),
n_neighbors = sqrt(dim(t(normalized.log.ex))[1]),#or the square root of the rows
min_dist = 0.1,
metric = "euclidean", #you can change it
n_components = 2) #used the default ones!
umap_df <- data.frame(umap_data$layout)
group_data <- data.frame(metadata$specimen.ch1)
umap_df <- cbind(umap_df,group_data)
colnames(umap_df) <- c("X1", "X2", "Group")
umap_df$Group<-c(rep("Reduction Mammoplasty", 18), rep("ER+ Breast Cancer",9), rep("ER- Breast Cancer", 9), rep("Prophylactic Mastectomy",6))
library(plotly)
figUmap <- plot_ly(umap_df,
x = ~X1, y = ~X2, color = umap_df$Group,
colors = c('cadetblue1', 'red','purple'),
type = 'scatter',
mode = 'markers',
size=1)
# Display the 2D scatter plot
figUmapumap_data_3D <- umap::umap(t(normalized.log.ex),
n_neighbors = sqrt(dim(t(normalized.log.ex))[1]),
#or the square root of the rows
min_dist = 0.1,
metric = "euclidean", #you can change it
n_components = 3) #used the default ones!
umap_df_3D <- data.frame(umap_data_3D$layout)
group_data <- data.frame(metadata$specimen.ch1)
umap_df_3D <- cbind(umap_df_3D,group_data)
colnames(umap_df_3D) <- c("X1", "X2", "X3", "Group")
umap_df_3D$Group<-c(rep("Reduction Mammoplasty", 18), rep("ER+ Breast Cancer",9), rep("ER- Breast Cancer", 9), rep("Prophylactic Mastectomy",6))
figUmap_3D <- plot_ly(umap_df_3D,
x = ~X1, y = ~X2, z=~X3, color = umap_df_3D$Group,
colors = c('cadetblue1', 'red','purple'),
mode = 'markers',
size=1) %>% layout(title = 'Umap 3D')
# Display the 3D scatter plot
figUmap_3DClustering
K-means
set.seed(1)
k <- 2 # number of clusters
kmeans_result <- kmeans(t(normalized.log.ex),k)
table(kmeans_result$cluster) # tells how many samples were assigned to each cluster##
## 1 2
## 14 28plot(kmeans_result, data=t(normalized.log.ex)) + geom_text(aes(label=metadata$disease.state.ch1),hjust=0,vjust=0)
fviz_cluster(kmeans_result, data = t(normalized.log.ex),
palette = c("#FF6666", "#33cccc"),
geom = "point",
ellipse.type = "convex",
ggtheme = theme_bw()
)
Let’s try increasing the number of clusters.
set.seed(1)
k <- 4 # number of clusters
kmeans_result <- kmeans(t(normalized.log.ex),k)
table(kmeans_result$cluster) # tells how many samples were assigned to each cluster##
## 1 2 3 4
## 8 4 6 24plot(kmeans_result, data=t(normalized.log.ex)) + geom_text(aes(label=metadata$specimen.ch1),hjust=0,vjust=0)
#fviz_cluster(kmeans_result, data = t(normalized.log.ex),
# palette = c("#2E9FDF", "#E7B800", "green", "red"),
# geom = "point",
# ellipse.type = "convex",
# ggtheme = theme_bw()
# )
fviz_cluster(kmeans_result, data = t(normalized.log.ex),
palette = c("#FF6666", "#99C666", "#33cccc", "#cc66ff"),
geom = "point",
ellipse.type = "convex",
ggtheme = theme_bw()
)